Action |
Hit ”˜12’ | Stick ”˜12” | |
Player Wins |
34.87% |
35.67% | |
Player Loses | 60.22% | 64.33% | |
Push | 4.91% | 0.00% |
I’ve spent the last few weeks asking my readers to not just break the slot habit, but utilize proper strategy for whatever other game they choose to play.
Development of strategy is not done by playing hunches. It is created by analyzing each play situation mathematically and determining the best action that can be taken to maximize the chances to end up a winner. Sometimes the math can be a bit confusing and this has led some people to try and sell the players snake oil instead of sound strategies.
The reality is that you don’t have to understand all (or any) of the math in order to utilize proper strategy. I haven’t a clue as to why my car moves forward when I hit the gas pedal, but that doesn’t mean I don’t trust or use my car. I know that there are engineers who created the car engine, so I just need to rely on the end product.
In similar fashion, you simply need to trust that the mathematician (me!) knows what he’s doing.
That said, this doesn’t mean that you shouldn’t have some confidence in how we go about analyzing a game and determining the best strategy. The concept of "trust me, because I said so," should only go so far, or only after someone has proved himself worthy of such trust. So, let’s take a look at a simple example first. What is the correct strategy for playing a 12 against a Dealer ”˜2’ (upcard) and why?
Step 1 in the process would be that we would agree that whatever strategy results in the Player winning the most money (or losing the least money) is the correct strategy. If for some reason the goal were to bust the least number of times, then our answer might be a bit different.
There are essentially two ways we can determine the answer. The first would be a purely mathematical model which would look at the probabilities of drawing each possible card by both the Player and the Dealer and the likelihood of winding up with each possible final hand value (including a bust).
I leave these models to the PH.Ds in math and prefer the second solution — a simple computer simulation that will play this situation a few hundred thousand times and give me the answer.
The simulation gave us the following results:
Without having set up the criteria for what determines the right strategy, we would be rather confused at the moment. We both win more often and lose more often by sticking on the 12. It is not possible to push in these cases. But what matters is money, not the number of hands won or lost.
When we apply real money to these percentages, we find that the Player who hits a 12 against a 2 will win 74.65 cents of every dollar wagered, while the Player who sticks will win back only 71.33 cents of every dollar wagered. The proper play is to hit the 12.
The bad news is that in the long run, the Player is going to lose far more often than he will win on this hand. However, reducing your losses on hands like these are as much a part of long term winning as is maximizing your profits on hands in which you have the advantage.
In theory, I should also run the simulation to test out the strategy of Doubling Down. I know from my experience of analyzing blackjack, that Doubling Down is definitely not the right strategy for this case.
Just over 3 cents may not seem like a large difference, but this equates to 16.5 cents per $5 hand. If we assume 30 hands per hour, you’ll be costing yourself about $5 per hour. This particular case is also one where the difference between hitting and sticking is relatively small.
In many cases, it might be 15 or 20 cents per dollar wagered difference. Playing those hands incorrectly will eat away at your bankroll that much faster. Blackjack can have a payback of about 99.6 percent (depending on the rules in use). However, that’s only if you play each hand correctly.
Incorrect play can easily bring the expected payback down to 98 percent or less, which put another way means increasing the house advantage by 400 percent or more!
Next week, I’ll cover how strategy is determined for video poker.